Computer with trojan

I just was looking at a firewall and noticed that one of the computers
was spitting out random requests to various computer ip addresses. I
think that this is a pretty good sign that the computer has a trojan
of some sort. Is there a way to track which program is creating this
activity and get rid of it.
I'm not exactly sure how this system got hacked. It has a firewall and
anti-virus and is not used for email. The only thing I can think of
was that skype was installed on it sometime back for testing purposes.
The only thing I can thing of currently is to turn off all programs
which are allowed to connect to the internet and see which ones start
trying to converse and then gradually allowing ones I'd expect to be
acceptable.
Is there some software out there that would track which program is
trying to communicate on the internet and trace the program.
It doesn't seem to be that smart of a program, because it just keeps
sending out these request to random IP's and ports. I would think
that this might be a lot harder if it was doing this about once every
five seconds instead of about 3 times per second.